Download Geometry 4-6 Analyzing Isosceles Triangles A. Isosceles Triangles 1

Geometry 4-6 Analyzing Isosceles Triangles
A. Isosceles Triangles
1. Theorem 4-6 Isosceles Triangle Theorem
-If two sides of a triangle are congruent, then the ________ opposite those
Q
sides are ______________.
Ex. 1: Proof of 4-6
Given: PQR, PQ ≅ QR
Prove: ∠ P ≅ ∠ R
S
Statements
1.) Let S be the midpoint of PR
2.) Draw auxiliary segment QS
3.) PS ≅ RS
4.) QS ≅ QS
5.) PQ ≅ QR
6.) PQS ≅ RQS
7.) ∠ P ≅ ∠ R
P
R
Reasons
1.) Every segment has exactly 1 midpoint.
2.) Through any two points there is one line
3.)
4.)
5.)
6.)
7.)
Ex. 2: In isosceles ISO with base SO. If m ∠ S = 2x + 40, and m ∠ F = 3x + 22,
find the measure of each angle of the triangle.
O
S
I
2. Theorem 4-7
-If two angles of a triangle are congruent, then the _________ opposite
those angles are _____________.
3. Corollary 4-3
-A triangle is equilateral if and only if it is equiangular.
4. Each angle of an equilateral triangle measures 60°.
HW: Geometry 4-6 p. 219-221
9-29 all, 35-37 all, 42-43, 45 (two column), 52-54 all